Only time I had a real emergency, it was on a boat. My cousin called the Coast Guard, politely. They came back with all kinds of questions: have you got your lifejackets on? what is your social security number? have you got the correct number of flares on your boat? etc etc etc. So I asked her for the mike and said the magic words: Mayday, Mayday Mayday!
Instantly everything changed; we had a senior chap come on frequency who sent us a helicopter and a cutter, which solved our problem eventually, but on a boat you have plenty of time thinking you are going to die. On a plane very little time, in this case, when ATC thought it was a hoax.
This, by the way, was off Galveston, Texas. They did understand the term I used, which in my case arose from my UK radio training. Incidentally, we were told later, after the rescue, that the Coast Guard had been plagued by shrimpers making hoax calls and they thought ours was also a hoax....which is why we had the initial runaround.